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- Analytic aspects of Poissonian white noise analysisPublication . Kondratiev, Yuri G.; Kuna, Tobias; Oliveira, Maria JoãoGeneral structures of Poissonian white noise analysis are presented.Simultaneously, the theory is developed on Poisson and Lebesgue- Poisson space. Both spaces have an own S-transform, well known in the Gaussian case. They give an extra connection between these two spaces via the Bargmann-Segal space. Test and generalized functions,different types of convolutions, and representations of creation and annihilation operators in the aforementioned spaces are considered.
- Extension of explicit formulas in Poissonian white noise analysis using harmonic analysis on configuration spacesPublication . Kondratiev, Yuri G.; Kuna, Tobias; Oliveira, Maria JoãoHarmonic analysis on configuration spaces is used in order to extend explicit expressions for the images of creation, annihilation, and second quantization operators in L2-spaces with respect to Poisson point processes to a set of functions larger than the space obtained by directly using chaos expansion. This permits,in particular, to derive an explicit expression for the generator of the second quantization of a sub-Markovian contraction semigroup on a set of functions which forms a core of the generator.